We study a telecommunications network integrating stream calls and elastic calls that share a given number of available traffic channels. The prioritised speech calls are handled as in a traditional Erlang loss model, while the delay-tolerant elastic calls are served with the remaining (varying) service capacity according to a processor sharing (PS) discipline. The remarkable observation is presented and analytically supported that the expected elastic call holding time is decreasing in the variability of the elastic call size distribution. This phenomenon is demonstrated for both Weibull and Pareto elastic call size distributions. Since the reverse effect is known to hold if elastic calls are served in a first-in first-out (FIFO) manner, an extended model is considered which limits the number of service positions in the elastic calls’ PS queue and holds excessive calls into a feeding FIFO queue. The impact of the elastic call size variability is demonstrated to depend on the number of service positions in the PS queue, as this determines whether the ‘PS’ or the (reverse) ‘FIFO effect’ is dominant. As a consequence of the principal result, network planning guidelines or admission control schemes that are developed based on deterministic or lightly variable elastic call sizes are likely to be conservative and inefficient, given the commonly acknowledged property of e.g. WWW documents to be heavy-tailed. Application areas of the models and results include fixed TCP/IP or ATM networks and mobile cellular GSM/GPRS and UMTS networks.
- Performance analysis
- Varying service capacity
- Quality of Service
- Heavy tail distributions Processor sharing models
- Integrated services networks